Multiscale Characterization and Model for the Dynamic Behavior of Ferroelectric Materials Using Fractional Operators

A Unique Fractional Derivative Operator to Simulate All Dynamic Piezoceramic Dielectric Manifestations: From Aging to Frequency-Dependent Hysteresis

“…In the Cole-Cole approach, α, the fractional order is linked to the distribution of relaxation time. Assuming E and P harmonictype waveforms, it is possible to establish a link between the dielectric spectroscopy Cole-Cole model and the fractional derivative high amplitude field consideration described previously [39] [40]. After analysis t of the equation an interesting relation between τ, α, ρ, and εs becomes apparent:…”

“…Comparisons between experimental results using the fractional Cole-Cole equation and simulations on Cole-Cole-type plots for classic PZT ceramic are available in literature [40] and can be used as validation of the fractional used under weak amplitude excitation. Havriliak-Negami advanced theory is sometimes necessary to gain high correlation between experimental and simulated results.…”

“…In past work [40] comparisons between simulations and experimental results are given for property is particularly interesting in our case because it means that even if the electric field excitation becomes null, as it is the case during aging, the polarization value will still evolve because of the memory of the previous states. The aging simulation is consequently based on eq.…”